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A conjecture on the free distance of (2,1,m) binary convolutional codes

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 356))

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Abstract

It is shown that the fixed binary (2,1,m) convolutional codes satisfy the Costello bound if two conjectures on the weight distribution of binary shortened cyclic codes are true.

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References

  1. D. Costello, Jr., Free distance bounds for convolutional codes, IEEE Trans. Inform. Theory, 20, pp. 356–365, 1974.

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  2. G.D. Forney, Structural analysis of convolutional codes via dual codes, IEEE Trans. Inform. Theory, 19, pp. 512–518, 1973.

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  3. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error Correcting Codes, North-Holland Publishing Company, Amsterdam, 1977.

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  5. Ph. Piret, On the number of divisors of a polynomial over GF(2), Applied Algebra, Algorithmics and Error-Correcting Codes, edited by A. Poli, Lecture Notes in Computer Science, 228, Springer-Verlag 1984.

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  6. W.J. Rosenberg, Structural properties of convolutional codes, Ph.D. Thesis, Univ. of California, Los Angeles, 1971.

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  7. Zigangirov, New asymptotic lower bounds on the free distance for time-constant convolutional codes, Problems of Inform. Transm., 22, pp.104–111, 1986.

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  8. G.D. Forney, Convolutional codes I: Algebraic structure, IEEE Trans. Inform. Theory, 16, pp. 720–738, 1970.

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Author information

Authors and Affiliations

  1. Philips Research Laboratory, 2, av. Van Becelaere, B-1170, Brussels, Belgium

    Ph. Piret

Authors
  1. Ph. Piret
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Editor information

Llorenç Huguet Alain Poli

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© 1989 Springer-Verlag Berlin Heidelberg

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Piret, P. (1989). A conjecture on the free distance of (2,1,m) binary convolutional codes. In: Huguet, L., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1987. Lecture Notes in Computer Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51082-6_93

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  • DOI: https://doi.org/10.1007/3-540-51082-6_93

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51082-6

  • Online ISBN: 978-3-540-46150-0

  • eBook Packages: Springer Book Archive

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